Calculus: Early Transcendentals 8th Edition

by
Stewart, James

Published by
Cengage Learning

ISBN 10:
1285741552

ISBN 13:
978-1-28574-155-0

Chapter 3 - Review - Exercises: 21

Answer

$y'=(3^{xln(x)})(ln(3))(1+ln(x))$

Work Step by Step

Start with the function $y=3^{xln(x)}$.
Apply exponential rule to differentiate: $y'=(3^{xln(x)})ln(3)(\frac{d}{dx}(x(ln(x))))$.
Use product rule to differentiate $xln(x)$:
$y'=(3^{xln(x)})(ln(3))(\frac{x}{x}+1*ln(x))$.
Simplify to arrive at the final answer: $y'=(3^{xln(x)})(ln(3))(1+ln(x))$.